OEIS A000184: Genus zero rooted maps with three faces

We explore A000184, the count of connected rooted planar maps on the sphere with exactly three faces. We unpack the genus-zero condition via Euler's formula, explain how rooting fixes symmetry, and show how a triple of permutations encodes vertices, edges, and faces. We’ll also touch on why number-theory-minded listeners should care: generating functions, Tutte equations with catalytic variables, bijections, and the connections these counts have to analytic combinatorics, topology, and even physics.

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